63 citations · 77 across the 7 of their papers we have counts for
8 papers
The conjecture of Ulam on the invariance of measure on Hilbert cube
Soon-Mo Jung
A conjecture of Ulam states that the standard probability measure on the Hilbert cube is invariant under the induced metric when the sequence of pos…
Dirac eigenvalues estimates in terms of symmetric tensors
Eui Chul Kim
We review some recent results concerning lower eigenvalues estimates for the Dirac operator [6, 7]. We show that Friedrich's inequality can be improved via certain well-chosen symm…
Some extensions of the Einstein-Dirac equation
Eui Chul Kim
We considered an extension of the standard functional for the Einstein-Dirac equation where the Dirac operator is replaced by the square of the Dirac operator and a real parameter…
Lower bounds of the Dirac eigenvalues on compact Riemannian spin manifolds with locally product structure
Eui Chul Kim
We study some similarities between almost product Riemannian structures and almost Hermitian structures. Inspired by the similarities, we prove lower eigenvalue estimates for the D…
Remark on the Limit Case of Positive Mass Theorem for Manifolds with Inner Boundary
Eui Chul Kim
In [5] Herzlich proved a new positive mass theorem for Riemannian 3-manifolds whose mean curvature of the boundary allows some positivity. In this paper we study what happ…
A Local Existence Theorem for the Einstein-Dirac Equation
Eui Chul Kim
We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold admitti…